Tax distortions cause a trade-off between efficiency and equity. However, taxes not only affect incentives; they also provide implicit insurance, and this may critically affect the efficiency–equity relationship. For a standard labour supply problem it is shown that the insurance effect mutes the sensitivity of labour supply to taxes, which tends to reduce tax distortions and lower the marginal costs of public funds. The relation between incentives and insurance and thus efficiency and equity is flattened by the insurance effect and it may even be non-monotone. However, the optimal utilitarian policy implies that there is always a trade-off between efficiency and equity on the margin.